Before describing our approach it is important to discuss shortly the physical meaning of the expression REF . As it describes field amplitudes of a single photon signal it is sometimes associated with a quantum wave function of a photon \(\Psi (r,t)\)  (as mentioned in [1]} and discussed in more details in [2]}, [3]}, [4]}). In this case \(|\Psi (r,t)|^2\)  has an intuitively clear meaning of the energy density of the photon. This or similar terminology is sometimes used in literature, including experimental papers [5]}, [6]}. This may stir some controversy related to localization problems of massless spin 1 particles first pointed out by Newton and Wigner [7]}. Interestingly though, this problem only appears for a spatial wave function, while in momentum (frequency) space the single photon wave function is a well defined mathematical object. Nevertheless, to avoid any terminology related confusions, in this paper we avoid using "single photon wave function", and refer to our experimental result, i.e. reconstruction of \(f_{k}(\omega _{k},t)\)  through multi-modal measurements of electric field, as "single photon portrait".
